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    <title>Delimiters</title>

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<h2>Delimiters</h2>


<p>Delimiters are objects which act logically like parentheses.

    These can be used only in math mode.</p>


<p>The delimiters recognized by LaTeX include</p>


<ul>

    <li><tt>(</tt> (left parenthesis)</li>

    <li><tt>)</tt> (right parenthesis)</li>

    <li><tt>[</tt> (left bracket)</li>

    <li><tt>]</tt> (right bracket)</li>

    <li><tt>\{</tt> (left brace)</li>

    <li><tt>\}</tt> (right brace)</li>

    <li><tt>|</tt> (vertical line)</li>

    <li><tt>\vert</tt> (vertical line)</li>

    <li><tt>\|</tt> (double vertical lines)</li>

    <li><tt>\Vert</tt> (double vertical lines)</li>

    <li><tt>/</tt> (slash)</li>

    <li><tt><a href="ltx-164.html">\backslash</a></tt> (backslash)</li>

    <li><tt>\langle</tt> (left angle bracket)</li>

    <li><tt>\rangle</tt> (right angle bracket)</li>

    <li><tt>\uparrow</tt> (uparrow)</li>

    <li><tt>\downarrow</tt> (down arrow)</li>

    <li><tt>\updownarrow</tt> (up/down arrow)</li>

</ul>


<h3><a name="big">Making delimiters the right size</a></h3>


<p>Delimiters in formulas should be big enough to "fit" around

    the formulas they delimit (for example arround arrays). To

    obtain "stretchable" delimiters (LaTeX makes them the

    appropriate size) type a <tt>\left</tt> or <tt>\right</tt>

    command before the delimiter. <tt>\left</tt> and

    <tt>\right</tt> commands must come in matching pairs, although

    the delimiters themselves need not be the same. Thus,</p>



<pre>

    \left \{ ... \right \[

</pre>


<p>produces a legal pair. In cases where only one delimiter is

    desired, it is possible to make the matching delimiter

    "invisible" by typing a period (<tt>.</tt>) after the command, i.e.,

    <tt>\left.</tt> or <tt>\right.</tt>.</p>


<p>In an <a href="ltx-223.html">eqnarray environment</a> the

    matching <tt>\left</tt> and <tt>\right</tt> cannot be split

    between lines and it may be necessary to use an "invisible"

    <tt>\right.</tt> and <tt>\left.</tt> to terminate and begin

    parts on different lines. In this case a second problem may

    arise, since the size of the delimiters will be chosen only for

    the <strong>local part</strong>, so that the size of the

    <strong>visible</strong> "left" and "right" delimiters might not

    match. The solution is to trick LaTeX into thinking that both

    parts have the same vertical height. This can be done by

    placing a strut, that is a zero-width

    <tt><a href="ltx-306.html">\rule</a></tt>. It can also be

    accomplished with the <tt>\vphantom</tt> command, which I have

    not found documented, but which appears to work.</p>



<pre>

    \vphantom{construct}

</pre>


<p>creates a zero-width object with the height of

    <tt>construct</tt>. The argument can contain things such as

    <tt><a href="ltx-235.html">\frac</a></tt> or the

    <a href="ltx-408.html">variable size math symbols</a> and

    should be chosen according to what is in the section with the

    delimiter you want to match.</p>


<h3>Some examples</h3>


<h4>A six-j symbol</h4>



<pre>

    \[ \left<a href="ltx-164.html">\{</a> 

     \begin{<a href="ltx-202.html">array</a>}{ccc} 

      a &amp; b &amp; c <a href="ltx-181.html">\\</a> 

      d &amp; e &amp; f \end{array}

     \right<a href="ltx-164.html">\}</a> \]

</pre>


<p>This should be displayed something like (insofar as it can be

    rendered in "ASCII art"):</p>



<pre>

    ( a b c )

    -       -

    ( d e f )

</pre>


<p>Note that the <tt>\[ ... \]</tt> set this off as

    <a href="ltx-421.html"> Display Math</a>, and that the

    <a href="ltx-202.html">Array Environment</a> is used to generate

    the three centered columns inside the braces.</p>


<h4>A "multiple choice" equation</h4>



<pre>

    \[ f(x) = 

      \left\{ \begin{array}{l} 

          0, x &lt; 0 \\ 1, x = 0 \\

          2, x &gt; 0 \end{array} \right. \]

</pre>


<p>will be displayed as</p>



<pre>

             ( 0, x &lt; 0

     f(x) =  - 1, x = 0

             ( 2, x &gt; 0

</pre>


<p>Note that the "invisible" <tt>\right</tt> delimiter is

    specified using a "period".</p>


<hr noshade="noshade" size="1">


<p>

    See also <a href="ltx-115.html">Math Formulas</a>,

    <a href="ltx-117.html">Math Symbols</a>

</p>


<ul>

    <li><a href="ltx-404.html">Binary and relational operators</a></li>

    <li><a href="ltx-115.html">Math formulas</a></li>

    <li><a href="ltx-202.html">Arrays</a></li>

    <li><a href="ltx-406.html">Arrows</a>

    <li><a href="ltx-408.html">Variable size symbols

        (sums, integrals, etc.)</a></li>

</ul>


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<p>

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